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Verify Stokes' Theorem for the vector field F(x, y, z) = −yi + xj - 2k where S is the part of the cone 2² = x² + y² with 0≤ ≤ 4, oriented upward, by computing the following: F. dr where C is the circle x² + y² = 16, z = 4, oriented counterclockwise (when viewed from above). (a) Compute 11² curl (F) dS, where S is the part of the cone z² = x² + y² with 0 ≤ z ≤ 4, oriented upward. (b) Compute

Verify Stokes' Theorem for the vector field F(x, y, z) = −yi + xj - 2k where S is the part of the cone 2² = x² + y² with 0≤ ≤ 4, oriented upward, by computing the following: F. dr where C is the circle x² + y² = 16, z = 4, oriented counterclockwise (when viewed from above). (a) Compute 11² curl (F) dS, where S is the part of the cone z² = x² + y² with 0 ≤ z ≤ 4, oriented upward. (b) Compute

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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12. Verify Stokes' Theorem for the vector field F(x, y, z) = -yi+ xj - 2k where S is the part of the cone 2² = x² + y² with 0≤ ≤ 4, oriented upward, by computing the following: (a) Compute F. dr where C is the circle x² + y² = (b) Compute 16, 24, oriented counterclockwise (when viewed from above). 11₁ curl (F) dS, where S is the part of the cone z2 = x² + y² with 0 ≤ ≤ 4, oriented upward.
Transcribed Image Text:12. Verify Stokes' Theorem for the vector field F(x, y, z) = -yi+ xj - 2k where S is the part of the cone 2² = x² + y² with 0≤ ≤ 4, oriented upward, by computing the following: (a) Compute F. dr where C is the circle x² + y² = (b) Compute 16, 24, oriented counterclockwise (when viewed from above). 11₁ curl (F) dS, where S is the part of the cone z2 = x² + y² with 0 ≤ ≤ 4, oriented upward.
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